Laminated composite parts are known, including (a) a first member having a predetermined mating surface, and (b) a second member that is made of an elastically deformable resin material, that has a plate portion substantially parallel to the mating surface and having a multiplicity of protrusions formed integrally therewith so as to protrude toward the mating surface so that space is created between the plate portion and the mating surface, and that is placed on the first member such that the protrusions contact the mating surface, the laminated composite parts having (c) cushioning properties as tip ends of the protrusions are pressed against the mating surface and elastically deformed, and (d) in which one of the first and second members which is located on a design surface side has an engaging projection that projects to a larger extent than the protrusions, and the engaging projection is inserted through an insertion hole formed in the other of the first and second members and is retained in the insertion hole, whereby the first and second members are connected together. A buffer structure described in Patent Document 1 is an example of such laminated composite parts. This buffer structure relates to an interior part for vehicles etc. A multiplicity of rib-like protrusions are provided on the back surface of an upholstery material (surface member) serving as the second member, whereby an excellent feel (soft feel) is provided by elastic deformation of the protrusions. Moreover, the engaging projection (attachment rib) provided on the back surface of the upholstery material is retained by the first member (core), whereby the upholstery material is prevented from being lifted regardless of the difference in thermal expansion.